Inverse Reconstruction of Cell Proliferation Laws in Cancer Invasion Modelling
Bibliographic record
Abstract
The process of local cancer cell invasion of the surrounding tissue is key for the overall tumour growth and spread within the human body, the past 3 decades witnessing intense mathematical modelling efforts in these regards. However, for a deep understanding of the cancer invasion process these modelling studies require robust data assimilation approaches. While being of crucial importance in assimilating potential clinical data, the inverse problems approaches in cancer modelling are still in their early stages, with questions regarding the retrieval of the characteristics of tumour cells motility, cells mutations, and cells population proliferation, remaining widely open. This study deals with the identification and reconstruction of the usually unknown cancer cell proliferation law in cancer modelling from macroscopic tumour snapshot data collected at some later stage in the tumour evolution. Considering two basic tumour configurations, associated with the case of one cancer cells population and two cancer cells subpopulations that exercise their dynamics within the extracellular matrix, we combine Tikhonov regularisation and gaussian mollification approaches with finite element and finite differences approximations to reconstruct the proliferation laws for each of these sub-populations from both exact and noisy measurements. Our inverse problem formulation is accompanied by numerical examples for the reconstruction of several proliferation laws used in cancer growth modelling.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".